You *can* ride in the rain, but alway follow your vendor’s recommendations. Most rental ECVs will come with a “shower cap” that fits over the controls to protect the electronics. Be sure to use it, and if you lose it, ask at your hotel for a shower cap - they usually have one to give you.
Def want to have a poncho, to cover you and as much of the scooter as possible; I do that by sitting on the scooter, and put the back of the poncho over the seat back (so it drapes down the back of the seat behind the scooter) and then pull the front of the poncho over the controls, and drape it down the front side of the controls/steering on the front end of the
ECV. That covers the majority of you and the scooter with one poncho.
If the seat folds down, be sure to fold it when you park the scooter to help keep the seat bottom dry if possible. You can also drape your poncho over the seat and controls when you leave it - might want to bring a few clothes pins from home to help keep it from blowing off.
But again - can’t stress this enough - speak with your rental vendor about their policies and recommendations. They always have the last word.